Q2. - Algebra 2

Question

Write an inequality using the $>$ symbol whose solution set is graphed below.

Step-by-Step Solution

Answer

The inequality whose solution graph is given is $-2x>-6$

Step 1 - Observation from image

From given image, open circle on 3 denotes it is not included in the solution.

All real number to the left of 3 are the solution of required inequality.

So, solution is all real number less than 3.

Step 2 - Write properties of inequality

Properties of inequalities are written in following table:

Step 3 - Write an example

Let $x$ denotes the variable.

As solution is all real number less than 3, so inequality is $x<3$

But to write inequality using $>$ symbol, use multiplication property of inequalities.

Multiply both sides with same negative number will reverse the sign of inequality.

So multiply both sides by any negative number gives required inequality as shown below.

$\begin{array}{c}x<3\\ x\times \left(-2\right)>3\times \left(-2\right)\\ -2x>-6\end{array}$

Thus, inequality using $>$ symbol is $-2x>-6$